Mike Sawyer’s Blog

I’m not talking about our electoral process which presents a host of problems itself. Rather, it is the plurality voting method which turns healthy debate into incontrovertible dogma. This results in extreme divisiveness, dirty tricks and yes, even mass shootings and bombings….

Most of the research on voting methods focuses on whether or not the method is fair. This is really a moot point since any method is “by definition” fair if all candidates and voters are playing by the same rules. Plus there’s no guarantee that “being fair” gets the best results for either candidates or voters. A better question is,

How inclusive is our voting method?

To clarify this, let’s look at an example. Suppose you and a group of friends decide to go out to a movie. There are seven movies playing in town so you decide to vote on which one to see. The one with the most votes wins (plurality voting). Each voter considers only his own selfish motives in selecting the one he would most like to see. But various members of your group have already seen some movies on the list.

In a small group of friends, most of us would consider changing our vote to accommodate our friends. This would be a voluntary way for the group to be more inclusive. Unfortunately our national politics has degraded to the point where we can’t see the pain of other voters. The prospect of excluding them from the process only hardens our resolve. Wouldn’t be nice if there were a voting method that could do this automatically?

Plurality voting ranks right on the bottom of the inclusivity scale.

Near the high end of this scale is the “bad apple sort” developed be an American, Clyde Coombs. Each voter ranks his choices in order of preference. The ballots are tallied by successively removing the choice or candidate with the most last place votes. I have dubbed the Coombs method the “bad apple sort” because it’s easier to visualize how it works. It’s like successively throwing out the worst apple in the basket until only the prize apple remains. Just remember

It Eliminates the Worst First

Of course, the criterion for bad apples are quite limited so most ballots would be similar. Candidates may have many facets for voters to like or dislike so ballots in a political election would take on many patterns. The algorithm itself can resolve even the most complex elections.

Generally speaking a low “inclusivity score” will reward a plurality of voters (not necessarily a majority) all the spoils, while excluding the wishes of the others thus dividing the group. On the other hand a high inclusivity score weighs the wishes of all factions (including such as racial, ethnic and religious groups) in proportion to their numbers to find the right balance. A high score also leaves the fewest voters out in the cold to become organized dissidents. In other words we expect a high score to unite us.

Let’s see how this might work in an actual polarized election.

A polarized election can be easily identified in a ranked choice election because just two candidates share the vast majority of first place votes while the same two share a majority of last place votes with few hits in the middle. This gives any moderate candidates in the middle a tremendous advantage. The bad apple sort will eliminate one of the two polarized candidates (the one with the most last place votes) first. In the second elimination round, the election is no longer bi-polar but still mono-polar. That is we have eliminated one polar candidate but not his voters, who still dislike (perhaps hate) the other prominent candidate making him the next to be eliminated.

The mistake both of these candidates made was trying to be the most liked, when the “bad apple sort” selects the least hated. If you and I can figure that out, so could the candidates and they would adjust their campaign strategy accordingly. They would seek broader appeal reaching out to all sides (something we haven’t seen that in a while). Certainly going out of your way to insult opposing groups would be political suicide. Politics would become civil again.

The bad apple sort has often been ignored by mathematicians because of a perceived flaw in this method.

The thinking has been that if one candidate is favored by a majority of voters, any viable voting method must always elect that candidate. This is not the case for the bad apple sort. It is possible for a candidate to have a majority of first place votes and still be eliminated by having more last place votes than any other candidate. Rethinking this dilemma it does make sense that the candidate who is best for the majority may not necessarily be the best choice for the electorate as a whole. The fear that minorities would be suppressed was a major concern for our founding fathers. That fear is now being realized.

It’s just that we never considered that there might be an algorithm that could find the best choice for all voters as a group or that there might computing power to handle it.

Now that we have the power it should be a snap, right! Technically simple to do, politically arduous to implement and we are only at the starting point. We need to begin a dialog about fixing this problem now that we know we can. This argument is long overdue because polarization and divisiveness have become unbearable and a threat to democracies here and around the world.

It has made us susceptible to conspiracy theories, manipulation by foreign powers and fear mongering. I believe that even most Trump supporters know we have the most divisive President in our history and probably would change that part of his rhetoric if they could. I’m sure they would also understand that Trump could never be reelected in a bad apple sort election. This doesn’t matter because realistically this kind of change cannot be achieved in less than five years. If fact, even with our best efforts we may already be too late.

We are not trying to change human nature. Instead we are capturing more information about each voter’s wishes. With ten candidates on the ballot, a plurality vote allows only ten ways to complete it while ranked choice voters have over a billion ways to complete the same ballot. We then use the bad apple sort to find the candidates and issues that best resonate with the electorate as a whole.

It is though the magic of the bad apple sort that we will find our true center.